Homotopy analysis method: A new analytic method for nonlinear problems

In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Differem from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.